Definition 1 Let n and k be positive integers such that 1 ≤ k ≤ n. The k-th ... network with two distinguished vertices s (start) and t (terminal), then we refer to the function ... complexity of Boolean functions in the Turing machine model (see [W,
Feb 1, 2008 - assume w.l.o.g. that any circuit for matrix product is a quadratic circuit ...... 1999, New York City, New York,, pages 45â50, 1109 Spring Street, ...
this paper we apply the same idea to obtain lower bound statements for a variety ... bounds in computational geometry (e.g. convex hull [5], slope selection [3]) de- ..... describes the canonical input, but with the last n line numbers permuted ac- .
Jul 13, 2016 - ANDREI GABRIELOV AND NICOLAI VOROBJOV. Abstract. We prove that the depth of any arithmetic network for deciding membership in a ...
Feb 15, 2015 - ON TOPOLOGICAL LOWER BOUNDS FOR ALGEBRAIC. COMPUTATION TREES. ANDREI GABRIELOV AND NICOLAI VOROBJOV. Abstract.
Jul 15, 2017 - Submitted to SODA 2018 â July 12, 2017 ... CG] 15 Jul 2017 ... Epifanov [15] proved that any planar graph with two special vertices called ...
Lower bounds for approximate factorizations via semidefinite programming (extended abstract)*. Erich Kaltofen,1 Bin Li,2 Kartik Sivaramakrishnan,1 Zhengfeng ...
bounding algorithm is deterministic if it is always guaranteed to output a lower or an upper bound. On the ..... Input: A graphical model G = ãX,D,Fã, a proposal distribution Q, an integer N and a real number 0 ⤠α ⤠1 ..... cutoff α = 100K
Abstract. We establish a lower bound of (1:12 ? o(1))nlogn on the size of any n-input sorting network; this is the rst lower bound that improves upon the trivial.
of dictionary learning for tensor data can be significantly lower than that for ...... [6] J. Mairal, F. Bach, and J. Ponce, âTask-driven dictionary learning,â. IEEE Trans ...
from real algebraic geometry due to Milnor [11] and Thorn. [23] that bounds the "topological complexity" of real al- gebraic varieties. Except for this result the ...
concept C to be learnt such that the expected error of gn is at least a constant times ...... class of concepts, and let f ng be a sequence of positive numbers.
the Average Query Complexity of a linearity test. Our proof ... A linearity test (over the field F2 for example) is a randomized algorithm which has oracle access .... x(v0), ...,x(vkâ1. ), then when running T on any linear function, the value of f
Oct 9, 2018 - Equality holds in (6) if and only if G is isomorphic to Kn. Proof. ..... [9] K. C. Das, S. A. Mojallal, Relation between energy and (signless) Lapla-.
Mar 9, 2007 - knots, preprint available at arXiv:math.GT/0503190. [IM0510] K. Ichihara and S. Mizushima, Crossing number and diameter of boundary slope ...
litical letters supposedly written in 1884 were actually ... words which defy unconditionally correct identification. ... for constructing codes: the center chooses a subset V .... the above expression over all j â {1,... ,c + 1} and dividing ... W
Oct 29, 2012 - Imre Bárány and Shmuel Onn, Colourful linear programming and its relatives, ... Department of Mathematics, Simon Fraser University, British ...
Nov 4, 2004 - integer multiplication (IMUL), and the discrete Fourier transform (DFT). ...... Karatsuba [19] gave a divide-and-conquer multiplication algorithm.
Apr 4, 2011 - Fifth, we show exponential lower bounds for the model checking ... the domain of f and ran(f) = {y ∈ B | ∃x ∈ A.f(x) = y} the range of f. By the ..... approximated to any factor in polynomial time (polynomial in the .... with 7x1 + 5x2
Oct 26, 2010 - TOBIAS H. COLDING AND WILLIAM P. MINICOZZI II ... where C comes from the Bishop-Gromov volume comparison (see page 275 of [G]) and.
spectral norm A = max{Ax | x â Cn, x = 1 } by choosing x smartly. Here · applied to a vector denotes the Euclidean norm. Key words and phrases: Spectral norm, ...
Oct 11, 2006 - 2000 Mathematics Subject Classification. Primary 13A50. Key words and phrases. Modular invariant theory, vector invariants, degree bound.
Apr 30, 2015 - knowing Hf on J? Figure 1. A function f on [0, 1] with HfL2([2,3]) â¼ 10â7 fL2([0,1]). 1. arXiv:1311.6845v4 [math.CA] 30 Apr 2015 ...
any bounded-width branching program computing a nonconstant threshold ... bounds on the length of bounded-width branching programs to solve certain ...
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